Particle transport problems have high dimensionality; Discretization of the BTE in the phase space and time results in a problem with a very large number of degrees of freedom (DoF).
This has stimulated active research on the development of ROMs for the BTE and its related class of problems
[1]}, [2]}, [3]}, [4]}, [5]}.
In this study, the new ROMs for TRT problems (REF )-(REF ) are based
on the proper orthogonal decomposition (POD) and projection approach [6]}, [7]}, [8]}.
The POD creates an optimal basis to represent dynamics of a system
based on a set of collected data [9]}.
Specifically, the reduced basis for a Galerkin expansion of intensities over the phase space is generated by the POD of a collection of
vectors of numerical transport solutions over time intervals of the TRT problem.
The BTE is projected onto this basis.
The POD-Galerkin projected BTE can be viewed as a discretization scheme based
on a set of problem-specific global basis functions.
The projected BTE is then coupled with the multilevel
nonlinear system of governing moment equations consisting of (i) low-order quasidiffusion (aka VEF) equations for the group and total radiation energy densities and fluxes and (ii) MEB equation.
The moment equations are derived by a nonlinear projection of the BTE (Eq. (REF ))
using exact closures by means of quasidiffusion (Eddington) factors.
The POD-Galerkin expansion of intensities is used to compute the quasidiffusion (QD) factors.
